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Mashcka [7]
3 years ago
9

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perim

eter of ∆ABC; 2) The area of ∆ABC; 3) The height to the hypotenuse.
I need to find the height please help
Mathematics
1 answer:
8090 [49]3 years ago
7 0
1- getting the side lengths:
We are given that the ratio between the sides is:
BC : AC : AB
4    : 3    : 5
We are also given that AC = 12 cm
We will simply use cross multiplication to find the lengths of the other two sides as follows:
BC : AC : AB
4    : 3    : 5
??  : 12  : ??
length of BC = (12*4) / 3 = 16 cm
length of AB = (12*5) / 3 = 20 cm

2- getting the perimeter of the triangle:
perimeter = AB + BC + AC
perimeter = 20 + 16 + 12
perimeter = 48 cm

3- getting the length of the hypotenuse:
We are given that angle C is the right angle in triangle ABC. The hypotenuse is the side opposite to the right angle. In our case, this side is AB.
This means that the length of the hypotenuse = AB = 20 cm

4- getting the area of the triangle:
area of triangle = 0.5 * base * height
Since the given triangle is a right-angled triangle, therefore, the base and the height are the two legs associated with the right angle.
This means that:
base = AC = 12 cm
height = BC = 16 cm
Therefore:
area of triangle = 0.5 * 12 * 16 = 96 cm²

Hope this helps :)
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How do you tell if it's possible to make a triangle out of these side lengths?<br> PLZ HELP!!!!!
Nastasia [14]

Answer:

A

Step-by-step explanation:

square root of 73 is about 8.5

square root of 10 is about 3. multiply by 3, you get 9.

square root of 7 is about 2.6. multiply by 5, you get 13.

when determining if you can make a triangle, if all variants of two sides can add up to be greater than the third side, you can make the triangle. so 8.5+9 > 13; 13+9 > 8.5; 13+8.5 > 9. this means it can make a triangle and all you have to do is order the sides.

8.5 is smallest which corresponds to angle c because it's opposite. 9 goes to angle a, then finally 13 goes to angle b. thus, angles c, a, b is the order.

side note: the smallest side length will always correspond with the smallest angle.

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